Out with the monkey and in with the rooster – Chinese New Year (CNY) is approaching, and the way Singaporeans usually celebrate it, is with sinful steamboat feasts, red packets and a litmus test for the year’s luck over a game of Blackjack.
Instead of leaving the fate of our money entirely to luck this year, we decided to do some research on the probability of winning a Blackjack round. We hope that would tilt the game in our favour.
Just so everyone is on the same page game, we will be playing the Singaporean CNY style of Blackjack, where each player, including the dealer, is given two cards, both placed downwards. This is unlike that of many casinos where the dealer usually reveals one of his two cards allowing players to better calculate their odds of winning. Each player must also have at least a minimum of 16 points for their hand. We will also assume that each game is played with just 1 deck of cards.
Before we start, we want it to be known that none of us on the team are card gamblers, nor are we addicted to any form of gambling (i.e. TOTO, 4D, football betting, etc), hence we are no experts and the advice we are giving is all in the name of CNY fun. If you lose more money this year following our advice, please blame it on your poor luck instead.
Probability of a “ Good Initial Hand”
Firstly, the total number of combinations we can obtain is calculated by:
C (Total number of cards, 2) = C (52,2) = 1326
The probability of obtaining a Blackjack is therefore calculated by:
(No. Of Ace x No. Value 10 cards) / (Total No. Of combinations) = (4 x 16) / 1326 = 4.83%
We can go on and do the same for the rest of the combination:
Probability of getting a 20 from the first two cards: 136 / 1326 = 10.26%
Probability of getting a 19 from the first two cards: 80 / 1326 = 6.03%
Probability of getting a 18 from the first two cards: 86 / 1326 = 6.49%
Probability of getting a 17 from the first two cards: 96 / 1326 = 7.24%
The total chance of obtaining a good initial hand (17 & above) is about 34.85%.
Obtaining 17 points and above is a good hand statistically, due to the good odds of beating the dealer without taking on additional risk.
Out of the remaining 65.15%, players are usually met with either of the 2 scenarios.
# 1 Player has an initial hand of 15 points and below
Since every player has to have a minimum of 16 points to remain in the game, player falling into such category must take a card or more. The higher your current points, the higher your chances of going bust in your next draw, with 15 points being the worst possible initial hand you can draw. There is nothing much you can do at this point except keep drawing until you hit at least 16, or go bust (above 21).
# 2 Player has an initial hand of 16 points
Given that 16 points is the minimum point to stay in the game, players with 16 points are met with a dilemma of whether or not to draw an additional card. Here’s one way of assessing the scenario.
If you draw an initial hand of 16, it means that the probability of the dealer being ahead of your after the initial hand (i.e. 17 or above) is only about 35%. Do note this does not mean your chances of winning the round are 65%.
Assuming a game only between you and the dealer. Chances of you drawing a card value 5 or less is definitely lower than 50% due to the high number of value 10 cards. That means there is a great chance you will go bust if you do draw another card, regardless of what the dealer do. In other words, your chance of winning goes down significantly if you do draw an additional card.
With that said, a rational player should not draw when he obtains an initial hand of 16.
Calculating the probability of getting the card you want
The ultimate strategy to winning in Blackjack is based on counting the number of cards played.
For players, communicating with each other for better flow of information can help with calculating the probability of obtaining a favorable value. However, your dealer friend may not like this idea. And if you were to try this at the casino, you would be lucky if the only thing that happens to you is just getting thrown out.
Assuming you were hoping to get a 4 for your next card, the probability for obtaining a 4 is as such:
(4 minus no. of 4s that are already out) / (52 – Total no. of cards that are already out)
For the probability of obtaining a card with value 10 (which includes J, Q, K), the probability is as such:
(16 minus no. of 10s that are already out) / (52 – Total no. of cards that are already out)
We are not supporters of gambling. But if you are going to play anyway this CNY, we think you should at least try to improve your chances of winning.